Fostering Representational Flexibility in the Mathematical Working Space of Rational Numbers

Abstract

The study focuses on the cognitive level of Mathematical Working Space (MWS) and the component of the epistemological level related to semiotic representations in two mathematical domains of rational numbers: fraction and decimal number addition. Within this scope, it aims to explore how representational flexibility develops over time. A similar developmental pattern of four distinct hierarchical levels of student representational flexibility in both domains is identified. The findings indicate that the genesis of the semiotic axis in fraction and decimal addition is not automatic, but a long process of developmental steps that could be referred to as MWS1, MWS2, MWS3, MWS4 (final). There is not a clear and stable correspondence between developmental levels of representational flexibility and school grades. Didactical implications in order to foster representational flexibility in the MWS of fraction and decimal addition are discussed.Key words: Representational Flexibility. Mathematical Working Space. Fractions. Decimals. ResumenEl estudio se centra en el nivel cognitivo del Espacio de Trabajo Matemático (ETM) y en el plano epistemológico relacionado con las representaciones semióticas en dos dominios matemáticos de números racionales: fracción y número decimal. Dentro de este ámbito, se pretende explorar cómo la flexibilidad representacional evoluciona en el tiempo. Se identificó un patrón de similar de desarrollo de flexibilidad de representación en los en ambos dominios.. Los resultados indican que la génesis semiótica en la fracción y la adición decimal no es automática, sino un largo proceso de pasos de desarrollo que podría denominarse como ETM1, ETM2, ETM3, ETM4. Sin embargo, no hay una correspondencia clara y estable entre los niveles de

How could the Presentation of a Geometrical Task Influence Student Creativity?

“…(e.g. Sierpinska, 1992;Gagatsis & Shiakalli, 2004;Duval, 2006;Gagatsis, Christodoulou, & Elia, 2013;Gagatsis, Deliyianni, Elia, Panaoura, & Michael-Chrysanthou, 2016;Nicolaou, Gagatsis, Panaoura, Deliyianni, Elia, & Televantou, 2020). It is also reported that the role of representations is very important in problem solving (Elia, Gagatsis, & Demetriou, 2007).…”